Classification

Standard classification problems

In a classification problem, we would typically have some input vectors x and some desired output labels y. Let's consider then a simple classification problem called the yin-yang problem. In this problem, we have to classes of elements. Elements belonging to the positive class, shown in blue; and elements belonging to the negative class, shown in red.

This data can be downloaded in Excel format here. In order to load this data into an application, let's use the ExcelReader class together with some extensions methods from the Accord.Math namespace. Add the following using namespace clauses on top of your source file:

using Accord.Controls;
using Accord.IO;
using Accord.Math;

Then, let's write the following code:

// Read the Excel worksheet into a DataTable
DataTable table = new ExcelReader("examples.xls").GetWorksheet("Sheet1");

// Convert the DataTable to input and output vectors
double[][] inputs = table.ToArray<double>("X", "Y");
int[] outputs = table.Columns["G"].ToArray<int>();

// Plot the data
ScatterplotBox.Show("Yin-Yang", inputs, outputs).Hold();

After we run and execute this code, we will get the following scatter plot shown on the screen:

Models

Naive Bayes

// In our problem, we have 2 classes (samples can be either
// positive or negative), and 2 inputs (x and y coordinates).

var nb = new NaiveBayes<NormalDistribution>(classes: 2,
    inputs: 2, prior: new NormalDistribution());

// The Naive Bayes expects the class labels to 
// range from 0 to k, so we convert -1 to be 0:
//
outputs = outputs.Apply(x => x < 0 ? 0 : x);

// Estimate the Naive Bayes
double error = nb.Estimate(inputs, outputs);

// Classify the samples using the model
int[] answers = inputs.Apply(nb.Compute);

// Plot the results
ScatterplotBox.Show("Expected results", inputs, outputs);
ScatterplotBox.Show("Naive Bayes results", inputs, answers)
    .Hold();

Support Vector Machines

Decision Trees

// In our problem, we have 2 classes (samples can be either
// positive or negative), and 2 continuous-valued inputs.
DecisionTree tree = new DecisionTree(attributes: new[] 
{
    DecisionVariable.Continuous("X"),
    DecisionVariable.Continuous("Y")
}, outputClasses: 2);

C45Learning teacher = new C45Learning(tree);

// The C4.5 algorithm expects the class labels to
// range from 0 to k, so we convert -1 to be zero:
//
outputs = outputs.Apply(x => x < 0 ? 0 : x);

double error = teacher.Run(inputs, outputs);

// Classify the samples using the model
int[] answers = inputs.Apply(tree.Compute);

// Plot the results
ScatterplotBox.Show("Expected results", inputs, outputs);
ScatterplotBox.Show("Decision Tree results", inputs, answers)
    .Hold();

Neural Networks

Logistic Regresssion

Variations

Multi-label problems

Sequence classification

How do I classify sequences with hidden Markov Models?